Federal Student Loan Refinancing Act This bill amends title IV (Student Assistance) of the Higher Education Act of 1965 to allow borrowers that received loans under the William D. Ford Federal Direct Loan (DL) or Federal Family Education Loan (FFEL) program on or after July 1, 2006, to consolidate those loans as Federal Direct Consolidation Loans. It directs the Department of Education (ED) to consolidate DLs, and send a completed loan consolidation application to FFEL borrowers, within 90 days of this bill's enactment. It gives FFEL borrowers six months after their receipt of such application to endorse it and submit it to ED if they wish to consolidate their loans. The bill sets the interest rate on Federal Direct Consolidation Loans at 4% or, if the weighted average of the interest rates of the loans being consolidated is less than 4%, the lesser of: (1) that weighted average, or (2) an interest rate equal to 0.4% of the principal balance of the consolidation loan at the time of consolidation. It adds an origination fee equal to 0.4% of the principal balance of the consolidation loan at the time of consolidation if an FFEL is being consolidated. It reduces the interest rate on a Federal Direct Consolidation Loan by 0.25% if one or more of the loans being consolidated is an FFEL held by an eligible lender. The bill prohibits any benefit a borrower is receiving or earning when issued a Federal Direct Consolidation Loan from being affected by the consolidation.